Sony HX300 has a 20.0MP 1/2.3-inch (6.16 x 4.62 mm ) sized BSI-CMOS sensor . On the other hand, Panasonic ZS8 has a 14.0MP 1/2.3-inch (6.08 x 4.56 mm ) sized CCD sensor and features Venus Engine FHD processor.
Sony HX300's sensor provides 6MP more than Panasonic ZS8's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the HX300 and ZS8 sensor size comparison.
Sony HX300 and Panasonic ZS8 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.